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Exam 5: Discrete Probability Distributions

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Question 91

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TABLE 5-6 The quality control manager of Green Bulbs Inc. is inspecting a batch of energy saving compact fluorescent light bulbs. When the production process is in control, the average number of bad bulbs per shift is 6.0. -Referring to Table 5-6, what is the probability that any particular shift being inspected has produced at least 6.0 bad bulbs.

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Question 92

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Thirty-six of the staff of 80 teachers at a local intermediate school are certified in Cardio-Pulmonary Resuscitation (CPR) . In 180 days of school, about how many days can we expect that the teacher on bus duty will likely be certified in CPR?

A) 5 days
B) 45 days
C) 65 days
D) 81 days

E) All of the above
F) A) and C)

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Question 93

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The Department of Commerce in a particular state has determined that the number of small businesses that declare bankruptcy per month is approximately a Poisson distribution with a mean of 6.4. Find the probability that more than 3 bankruptcies occur next month.

In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7, 11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The probability that she gets audited no more than 2 times is ________.

A national trend predicts that women will account for half of all business travelers in the next 3 years. To attract these women business travelers, hotels are providing more amenities that women particularly like. A recent survey of American hotels found that 70% offer hairdryers in the bathrooms. Consider a random and independent sample of 20 hotels. Find the probability that more than 7 but less than 13 of the hotels in the sample offered hairdryers in the bathrooms.

TABLE 5-5 From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed. -Referring to Table 5-5, what is the probability out of the 8 new cars it just received that, when each is tested, at least half of the cars have defective radios?

TABLE 5-7 There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: $\begin{array} { | c | c | c | } \hline & { \text { Returns } } \\\hline \text { Probability } & \text { Neighborhood A } & \text { Neighborhood B } \\\hline .25 & - \$ 22,500 & \$ 30,500 \\\hline .40 & \$ 10,000 & \$ 25,000 \\\hline .35 & \$ 40,500 & \$ 10,500 \\\hline\end{array}$ -Referring to Table 5-7, if you can invest 30% of your money on the house in neighborhood A and the remaining on the house in neighborhood B, what is the portfolio risk of your investment?

TABLE 5-8 Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants. Your profit (in thousands of dollars) will depend on the taste of the consumers when winter arrives. The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table. $\begin{array} { | c | c | c | c | } \hline \text { Probability } & \text { Taste } & \text { Design A } & \text { Design B } \\\hline 0.2 & \text { more conservative } & 180 & 520 \\\hline 0.5 & \text { no change } & 230 & 310 \\\hline 0.3 & \text { more liberal } & 350 & 270 \\\hline\end{array}$ -Referring to Table 5-8, if you decide to choose Design A for 70% of the production lines and Design B for the remaining production lines, what is the expected profit?

TABLE 5-7 There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: $\begin{array} { | c | c | c | } \hline & { \text { Returns } } \\\hline \text { Probability } & \text { Neighborhood A } & \text { Neighborhood B } \\\hline .25 & - \$ 22,500 & \$ 30,500 \\\hline .40 & \$ 10,000 & \$ 25,000 \\\hline .35 & \$ 40,500 & \$ 10,500 \\\hline\end{array}$ -Referring to Table 5-7, if you can invest 70% of your money on the house in neighborhood A and the remaining on the house in neighborhood B, what is the portfolio risk of your investment?

TABLE 5-7 There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: $\begin{array} { | c | c | c | } \hline & { \text { Returns } } \\\hline \text { Probability } & \text { Neighborhood A } & \text { Neighborhood B } \\\hline .25 & - \$ 22,500 & \$ 30,500 \\\hline .40 & \$ 10,000 & \$ 25,000 \\\hline .35 & \$ 40,500 & \$ 10,500 \\\hline\end{array}$ -Referring to Table 5-7, if you can invest 90% of your money on the house in neighborhood A and the remaining on the house in neighborhood B, what is the portfolio risk of your investment?

If n = 10 and π = 0.70, then the standard deviation of the binomial distribution is

TABLE 5-9 A major hotel chain keeps a record of the number of mishandled bags per 1,000 customers. In a recent year, the hotel chain had 4.06 mishandled bags per 1,000 customers. Assume that the number of mishandled bags has a Poisson distribution. -Referring to Table 5-9, what is the probability that in the next 1,000 customers, the hotel chain will have fewer than eight mishandled bags?

The quality control manager of a candy plant is inspecting a batch of chocolate chip bags. When the production process is in control, the average number of blue chocolate chips per bag is 6.0. Suppose that the probability of a blue chocolate chip in a bag is constant across bags and the number of blue chocolate chips in one bag is independent of the number in any other bag. Which of the following distributions would you use to figure out the probability that any particular bag being inspected has 4.0 blue chocolate chips?

TABLE 5-1 The probability that a particular type of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. You have 2 such alarms in your home and they operate independently. -Referring to Table 5-1, the probability that at least one sounds an alarm in the presence of smoke is ________.

Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that 2 or fewer prefer Brand C is ________.

TABLE 5-10 An accounting firm in a college town usually recruits employees from two of the universities in town. This year, there are fifteen graduates from University A and five from University B and the firm decides to hire six new employees from the two universities. -Referring to Table 5-10, what is the probability that all six of the new employees will be from University A?

What type of probability distribution will the consulting firm most likely employ to analyze the insurance claims in the following problem? An insurance company has called a consulting firm to determine if the company has an unusually high number of false insurance claims. It is known that the industry proportion for false claims is 3%. The consulting firm has decided to randomly and independently sample 100 of the company's insurance claims. They believe the number of these 100 that are false will yield the information the company desires.

The online access computer service industry is growing at an extraordinary rate. Current estimates suggest that 75% of the home-based computers have access to online services. Suppose 20 people with home-based computers were randomly and independently sampled. Find the probability that fewer than 10 of those sampled currently have access to online services.

TABLE 5-10 An accounting firm in a college town usually recruits employees from two of the universities in town. This year, there are fifteen graduates from University A and five from University B and the firm decides to hire six new employees from the two universities. -Referring to Table 5-10, what is the probability that more than four of the new employees will be from University A?

A national trend predicts that women will account for half of all business travelers in the next 3 years. To attract these women business travelers, hotels are providing more amenities that women particularly like. A recent survey of American hotels found that 70% offer hairdryers in the bathrooms. Consider a random and independent sample of 20 hotels. Find the probability all of the hotels in the sample offered hairdryers in the bathrooms.